1. Introduction

First, as hosts, we welcome you to Trigonometric
Identities--A Clever Way to Prove. If you are reading
this, we believe that you are interested in mathematics, or that you
want to improve your mathematics problem solving skill.

Well, mathematics is interesting and very powerful. A lot of people
have lost their confidence while studying it, however. Is math
hard? Maybe, it depends on how you look at it, and how you learn
it. 1 + 1 = 2? That's right. Is it easy? Yes. When you look at
the problem, at the same time, you know the answer. Let's try
3 + 5 + 7 = 15. Yes, it takes you a couple of more seconds to
think about it, but finally you know the answer. What we are trying
to say is that when we know the most basic things, or ideas, even
though a problem is more complicated, we still have good chances
to solve it. Equality proving is one of the most basic problems
in mathematics. If we know how the equality works, then we will
know how to evaluate, solve equations and so on.

Trigonometry has a lot of different kinds of formulas. Some of
them are really complex. This makes trigonometric problems a great
example to discuss. As students, we have heard our friends and
other students talking about math: "I can not do it."
"I do not know how to do it." or "It's too hard."
without even looking at and thinking about the problems. People
are really scared by mathematics.

In general, the structures of a trigonometry book are definitions,
formulas, and examples. Most are examples about how to apply formulas
directly to some problems and are only for those particular formulas.
This arrangement has some defects. For example, we can always
see some students who don't know how to start to prove an identity
without any hint even if they know every trigonometric formula.
Here at LWR, we try to complete all trigonometry
books. We are not giving you a bunch of questions. Instead, we
give you some general ideas to prove an identity, and by that
way we can improve your mathematics problem solving skills. We
try to help you make a big improvement in a short period of time.
We believe our ideas are the best, and we need you to prove that
we are the best.

Before we begin, you must ask yourself: "Do I really want
to improve my problem solving skills?" If the answer is yes,
then you are ready to go.